113k views
4 votes
Solve the system of equations using elimination: -3x-4y=-54 and x+y=15.

User Totocaster
by
6.7k points

2 Answers

1 vote

Answer:

the solution of the system is x = 18/5 and y = 27/5.

Explanation:

To solve a system of equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the x-variable:

(-3x - 4y) + (x + y) = -54 + 15

-2x - 3y = -39

Dividing both sides by -3, we get:

(2/3)x + (1/3)y = 13/3

This equation tells us that x is equal to 2/3 times the value of y. Substituting this expression for x in one of the original equations, we can solve for y:

-3(2/3)y - 4y = -54

This simplifies to:

(-6/3)y - 4y = -54

Combining like terms, we get:

(-10/3)y = -54

Dividing both sides by -10/3, we get:

y = 27/5

Substituting this value for y in the expression for x, we get:

x = (2/3)(27/5) = 18/5

Therefore, the solution of the system is x = 18/5 and y = 27/5.

User Jeruki
by
6.8k points
5 votes

Answer: x=6, y=9

(6,9)

Explanation:

Multiply x+y=15 by 3 to eliminate x

3(x+y)=15(-3)

3x+3y=45

-3x-4y=-54

-1y=-9

y=9

sub in 9 to y to get x

x+9=15

x=6

User Pedreiro
by
6.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.